GPL3 has a clause specifically to deal with this situation [1]
- Use with the GNU Affero General Public License. Notwithstanding any other provision of this License, you have permission to link or combine any covered work with a work licensed under version 3 of the GNU Affero General Public License into a single combined work, and to convey the resulting work. The terms of this License will continue to apply to the part which is the covered work, but the special requirements of the GNU Affero General Public License, section 13, concerning interaction through a network will apply to the combination as such.
So you can use GPL3 code in AGPL projects. The GPL3 portion of the code will still be licensed under GPL3, but the network interaction clause of the AGPL3 will apply to the project as a whole, including the GPL3 parts.